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Reaction networks can display a wide array of dynamics. However, it ispossible for different reaction networks to display the same dynamics. Thisphenomenon is called dynamical equivalence and makes network identification ahard problem to solve. We show that to find a strongly endotactic, endotactic,consistent, or conservative realization that is dynamically equivalent to themass-action system generated by a given network, it suffices to consider onlythe source vertices of the given network. In addition, we show that weaklyreversible deficiency one realizations are not unique. We also present acharacterization of the dynamical relationships that exist between severaltypes of weakly reversible deficiency one networks.

Source-only realizations, weakly reversible deficiency one networks and dynamical equivalence